Questions and Answers
What are the counting numbers?
What includes zero and counting numbers?
Which set of numbers includes negative numbers?
Any number that is considered an integer, natural, or whole number cannot contain ______ or ______.
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What are rational numbers?
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Which of the following is an example of irrational numbers?
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What does the set of real numbers include?
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The 6 properties of real numbers include: _____, commutative, associative, identity, inverse, distributive.
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The closure property of addition states that m + n is a real number.
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The commutative property of multiplication states that mn = nm.
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What is the identity property of addition?
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What is the formula for the area of a triangle?
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What is the perimeter of a rectangle formula?
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What does the symbol < represent?
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A ______ is two inequalities joined together by either an 'and' or an 'or'.
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What is the formula for the circumference of a circle?
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When you multiply or divide by a _____, the direction of the inequality sign switches.
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What is the difference between an algebraic expression and an algebraic equation?
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The order of operations in solving algebraic expressions is ______.
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What does the additive inverse of any number m refer to?
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What is the temperature conversion formula to convert Celsius to Fahrenheit?
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Study Notes
Number Sets
- Natural Numbers: Counting numbers starting from 1 (e.g., 1, 2, 3...).
- Whole Numbers: Include all natural numbers plus zero (e.g., 0, 1, 2, 3...).
- Integers: Encompass all whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3...).
Types of Numbers
- Rational Numbers: Can be expressed as the ratio of two integers; can terminate or repeat in decimal form (e.g., 2/3 = 0.6666..., 3/4 = 0.75).
- Irrational Numbers: Cannot be expressed as simple fractions and their decimal forms neither terminate nor repeat (e.g., π = 3.1415..., √2 = 1.414213...).
- Real Numbers: Include all types of numbers on the number line, combining natural, whole, integers, rational, and irrational numbers.
Properties of Real Numbers
- Closure Property: For any real numbers m and n, both m+n and mn result in real numbers.
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Commutative Property:
- Addition: m+n = n+m
- Multiplication: mn = nm
-
Associative Property:
- Addition: (m+n)+p = m+(n+p)
- Multiplication: (mn)p = m(np)
-
Identity Property:
- Addition: m+0 = m
- Multiplication: m×1 = m
-
Inverse Property:
- Addition: m+(-m) = 0
- Multiplication: m×(1/m) = 1 (where m≠0)
- Distributive Property: m(n+p) = mn + mp.
Algebraic Concepts
- Additive Inverse: The opposite of a number m is represented as -m.
- Reciprocal: The multiplicative inverse of a nonzero number m is 1/m.
- Algebraic Expressions vs Equations: An expression lacks an equal sign while an equation contains one.
- Order of Operations (PEMDAS): Parenthesis, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
Solving Equations
- Substitution: Used to verify solutions of linear equations.
- Isolate: To find the value of a specific variable, one must isolate it.
Geometry Formulas
- Temperature Conversion: F = (9/5)C + 32.
-
Area Formulas:
- Triangle: A = ½bh.
- Rectangle: A = bh.
- Trapezoid: A = ½h(b₁ + b₂).
- Circle: A = πr².
- Circumference of Circle: C = πd.
- Perimeter of Rectangle: P = 2b + 2h.
Inequalities
-
Symbols:
- < means less than.
-
means greater than.
- ≤ means less than or equal to.
- ≥ means greater than or equal to.
- Graphing: Linear inequalities in one variable are represented on a number line; open circles indicate < or >, closed circles indicate ≤ or ≥.
Compound Inequalities and Absolute Values
- Compound Inequality: Combines two inequalities using "and" or "or".
- Inequality Direction: Negating a number changes the direction of the inequality sign.
- Absolute Value: |x| represents the magnitude of x, disregarding its sign.
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